If your flights were booked on one ticket then usually the airline will not allow you to book something that won't work. An hour and a half is usually more than enough - and if for some reason, things go wrong and it was all booked on one ticket then the airline (I'm guessing Lufthansa) will be responsible for making it work and any adjustments needed.
Oreet: The trip was booked through American and they, too, assure me we should have enough time. Still I worry and really appreciate this forum and the kind responses of people such as yourself. Thank you, very much. Joyce
I wouldn't worry - I have made international connections that were booked through American - with 1:20 connect time - no problems. And like I said, if your flight is delayed then the airline - either American or Lufthansa is responsible for your making the next available flight and any other considerations involved.
If the flight was offered to you by American, and you didn't use the multi-city or buy two separate tickets, they are responsible for the connection, so they must feel that it is plenty of time.
I'll add my voice to the not to worry crowd, IF YOU FLIGHT is one ticket.
You won't have to deal with your luggage, but it is a long walk through the airport to get to where the flights to Israel leave from, it's a separate building: you go through security again and then down a hall into another (connected) building. It gave me the creeps, frankly. The timing is doable, but don't linger when you land, go straight to your gate to Tel Aviv. (Traveller tip: Go to the bathroom in the main terminal, if necessary. The bathrooms near the gate for flights leaving for Israel are not nearly as nice.)